Models, Computers and Structural Analysis
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Tenth LACCEI Latin American and Caribbean Conference (LACCEI’2012), Megaprojects: Building Infrastructure by fostering engineering collaboration, efficient and effective integration and innovative planning, July 23-27, 2012, Panama City, Panama. Models, Computers and Structural Analysis Alberto Gomez-Rivas University of Houston Downtown, Houston, Texas, USA, [email protected] George Pincus University of Houston Downtown, Houston, Texas, USA, [email protected] Jorge A. Tito University of Houston Downtown, Houston, Texas, USA, [email protected] ABSTRACT There are three basic components of the structural design problem: the real structure, the physical model, and the computer model. To avoid the typical problems of scale and similitude in the physical models, it is assumed that if the computer model predicts the behavior of the physical model, then it can also predict the behavior of the real structure. This method would be very useful in engineering education because by using models it is possible to allow students to visualize complex phenomena learned in theory but not seen in practice. The use of models in structural engineering is motivated by the work in small boxes performed by Karl Terzaghi; the current diminishing budgets in universities; and because the women students that worked with the models seem to have a better understanding of the basic structural principles. Keywords: ABS Model, Plastic Model, Structural Model, Grid, Alamillo Bridge 1. INTRODUCTION Structural Engineers graduating from the Structural Analysis/Design option in engineering technology program at the University of Houston-Downtown are exposed in their undergraduate education to courses in fluid dynamics where they learn about the immense difficulties of similitude in the construction of hydraulic models. During their professional careers, dealing with unusual structures they then tend to think about models but the idea is quickly abandoned because of difficulties of scale and similitude. This paper describes a different view of models used in structural engineering. This paper deals with three objects: the real structure, the computer model, and the physical plastic model. The relation of these three entities is important for the paper. The basic hypothesis is that if the computer can predict the behavior of the model it also can predict the behavior of the structure. Structural software based on finite element principles applies to any structure regardless of the size of the elements. The critical point then is to verify that the behavior of the model and the computer are in close agreement. Adjustments to the computer model and its assumptions may be required to obtain satisfactory results. The issue of similitude that complicates a relationship model structure is not present here because the relations are: computer with model and computer with structure. The computer is used to avoid the similitude problem that complicates immensely physical modeling of structures (Starvridis, 2010) After the computer has been properly tuned to predict the behavior of the model, it is reasonable to assume that the computer will be able to predict the performance of the real structure. To achieve this goal, the model must represent the structure in a reasonable manner. This paper describes the best practices to build models that represent the structure. The case of the model of the Alamillo Bridge is used to illustrate these principles. The proposed use of models in structural engineering is very useful in engineering education because the models allow students to see and experience phenomena that they have not seen in practice. In some branches of engineering, hydraulics for instance, it is possible to see the real world relation between variables. The effect 10th Latin American and Caribbean Conference for Engineering and Technology Panama City, Panama Refereed Paper #143 July 23-27, 2012 changes in velocity in a pipe can be visualized by the height of the fluid in a Pitot tube. This is not the case in structural engineering where the most important relation between loads and deformations is not visible due to the very small relative size of the deformations. Learning and comprehending structural engineering is a matter of faith in mathematical formulas without having physical experiences. The high values of the modulus of elasticity of materials used in civil structures and the normal proportion of the structural members do not allow for visualization of the deformations that are thousands of the dimensions of the members of the structure. In other cases, structures are made very rigid to avoid human discomfort as is the case of floors. Common people and freshman students do not believe that structures deform under loads. A first step in structural engineering education is to show students that structures deform in predictable manner under the action of loads. Three important reasons motivate the use of models in structural engineering. First, it should be remembered that the founder of Theoretical Soil Mechanics, Karl Terzaghi performed his fundamental research in a cigar box. Second, during times of diminishing budgets in universities, models can provide an economical approach to education and research in structural engineering. Third, women students seem to obtain a better understanding of the behavior of structures when models are used to illustrate basic principles of mechanics. The paper discusses selection of materials for construction of the models. The basic principle is to make the model behave as a magnifying lens to the deformation of structures under the application of loads. The figures presented in the paper illustrate ABS plastic model experimenting large deflections under the action of small loads. Other considerations indicate why ABS plastic is an ideal material for construction of models of structures. Simplicity of instrumentation is important for success in the use and applications of the model to comprehend structural behavior. Since the model is a device to magnify the deformations of the structure to visualize behavior, the measurements of deformations do not need to be electronic sensors that clutter understanding of the behavior. Simple mechanical deflectometers communicate well the value of the deformations. Considering that the model should be very flexible, it is not necessary to use specialized devices for the application of loads. Simple weights and pulleys allow for the application vertical and horizontal loads. Great accuracy can be obtained in weighting the loads before they are applied with ready available electronic balances. Several models are presented in the paper: A simple supported beam used to determine the material properties of ABS plastic and the rigidity of the connections, specialized models dealing with torsion, multistory frames, grids for floors, and the model of the Alamillo Bridge. Each one of the models is described in detail. 2. MODELS USING ABS PLASTIC 2.1 SIMPLY SUPPORTED BEAM The objective of the model is to magnify deformations in complex structures. This magnification allows for visualization and measurement of the deformations. Materials that meet the objective of magnification of deformations must have low modulus of elasticity (E). To model a real steel structure using steel elements would not serve the magnification and visualization objective, mainly because the deformations of this steel model would be too small. Figure 1a presents a model of a simple supported beam with large deflections due to the low modulus of elasticity of ABS plastic. The moduli of elasticity of common structural materials are very high, for example the value for Steel is 200 GPa and for concrete about 25 GPa. On the other hand, plastics such as ABS have values of about 3.50 GPa. The same beam made of plastic will deflect sixty times more than the steel one. Steel has an elastic linear range that extends almost to the yield point and covers the range of structures under the action of service loads. For the model, it is desirable to find a material with a good elastic linear range. Tests conducted for this project indicates that ABS has elastic linear behavior within the range necessary to present significant deformations in models. Figure 1b presents the load deflection graph for the simple supported indicating a linear elastic behavior up to the point of failure. The elastic linear behavior of ABS is interesting and valuable for testing of the models because this property guaranties that if the model is not broken the behavior is linear elastic. 10th Latin American and Caribbean Conference for Engineering and Technology Panama City, Panama 2 July 23-27, 2012 a) Beam tested in the weak axis b) Load vs. Deflection curve at 23oC Figure1: Flexure test of a simple supported beam Dimensional stability that is the uniformity of dimensions of the cross sections of structural shapes is an important characteristic for construction of reliable models. ABS structural profiles have great dimensional stability along the axis of the elements. The shapes have not fillets and the cross section is completely defined by straight lines. Filets connecting webs and flanges in most structural shapes contribute to the sectional moment of inertia and their measurements are complex because it involves the determination of the radius of curvature. Not having fillets and straight boundaries the dimensions are determined with digital micrometers of high precision. The area, moments of inertia, and other cross section properties are obtained easily from AutoCAD drawing. Complex structures worth to model involve rigid connections. These connections are welded or bolted in steel structures or cast in place connections between columns and frames in reinforced concrete. The material to be used in the model construction must provide the opportunity to build rigid connections. Research on the ability to weld plastic materials indicates that ABS glue and acetone provide connections that are as rigid as the connected elements. The beam presented in Figure 1a consists of two pieces welded with acetone and, as observed, it undergo to large deformations up to the point of rupture without failure of the connection.